Question

Calcium hydroxide is a strong base but is not very soluble ( Ksp = 5.02 X 10-6 ). What is the pH of a saturated solution of Ca(OH)2 ?

Answer 1

Answer : The pH of a saturated solution is, 12.33

Explanation : Given,

`K_(sp)` =
`5.02* 10^(-6)`

First we have to calculate the solubility of
`OH^-` ion.

The balanced equilibrium reaction will be:

`Ca(OH)_2\rightleftharpoons Ca^(2+)+2OH^-`

Let the solubility will be, 's'.

The concentration of
`Ca^(2+)` ion = s

The concentration of
`OH^-` ion = 2s

The expression for solubility constant for this reaction will be,

`K_(sp)=[Ca^(2+)][OH^-]^2`

Let the solubility will be, 's'

`K_(sp)=(s)* (2s)^2`

`K_(sp)=(4s)^3`

Now put the value of
`K_[sp}` in this expression, we get the solubility.

`5.02* 10^(-6)=(4s)^3`

`s=1.079* 10^(-2)M`

The concentration of
`Ca^(2+)` ion = s =
`1.079* 10^(-2)M`

The concentration of
`OH^-` ion = 2s =
`2* (1.079* 10^(-2)M)=2.158* 10^(-2)M`

First we have to calculate the pOH.

`pOH=-\log [OH^-]`

`pOH=-\log (2.158* 10^(-2))`

`pOH=1.67`

Now we have to calculate the pH.

`pH+pOH=14\\\\pH=14-pOH\\\\pH=14-1.67=12.33`

Therefore, the pH of a saturated solution is, 12.33